One inventory, three quotes
Quotes vary legitimately (crew, overhead, negotiation) and illegitimately (deliberate low-balling). The defense is standardization: one written inventory list (room-by-room, including the garage and the storage unit), sent to three companies, compared line by line. Quotes built on different inventories are not comparable — they are bait.
The binding question
Ask each company: "Is this a binding not-to-exceed estimate?" The answer sorts the market: companies that offer it have priced honestly; companies that dodge it plan to re-price when your goods are on their truck. The question costs nothing and filters half the risk in one sentence.
Reading the itemization
Legitimate quotes itemize: labor hours and rate, travel time, materials, stairs/long-carry fees, fuel surcharge, insurance valuation, and taxes. The vague "total move" number is where substitutions live. Valuation coverage deserves its own look — released valuation ($0.60/lb) means your $1,200 TV is worth $12 in a claim; full-value protection costs more and actually covers.